Quantum Thouless-Anderson-Palmer equations for glassy systems

Giulio Biroli and Leticia F. Cugliandolo
Phys. Rev. B 64, 014206 – Published 15 June 2001
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Abstract

We derive Thouless-Anderson-Palmer (TAP) equations for quantum disordered systems. We apply them to the study of the paramagnetic and glassy phases of a quantum extension of the spherical p spin-glass model. We generalize several useful quantities (complexity, threshold level, etc.) and various ideas (configurational entropy crisis, etc.) that have been developed within the classical TAP approach to quantum systems. The analysis of the quantum TAP equations allows us to show that the phase diagram (temperature versus quantum parameter) of the p spin-glass model should be generic. In particular, we argue that a crossover from a second-order thermodynamic transition close to the classical critical point to a first-order thermodynamic transition close to the quantum critical point is to be expected in a large class of systems.

  • Received 9 November 2000

DOI:https://doi.org/10.1103/PhysRevB.64.014206

©2001 American Physical Society

Authors & Affiliations

Giulio Biroli1,2 and Leticia F. Cugliandolo2,3,*

  • 1Center for Material Theory, Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854
  • 2Laboratoire de Physique Théorique de l’Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
  • 3Laboratoire de Physique Théorique et Hautes Energies, Jussieu, 4 Place Jussieu, 75252 Paris Cedex 05, France

  • *Unité Mixte de Recherche du Center National de la Recherche Scientifique et de l’Ecole Normale Supérieure.

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Vol. 64, Iss. 1 — 1 July 2001

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